1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: The Sum of a series with exponents

  1. Dec 15, 2008 #1
    1. The problem statement, all variables and given/known data

    Problem: Indicate whether the series converges or diverges. If it converges, find its sum.



    2. Relevant equations

    The ratio test and w/e equation is used to find the sum of this particular series

    3. The attempt at a solution

    I was able to find that the series converges, using the ratio test. However, I cannot find the sum of the series. I do not see any way in which I could manipulate the geometric series, or anything like that. Could someone please enlighten me on how to find the sum of this series, or any series in such a form.
  2. jcsd
  3. Dec 15, 2008 #2


    User Avatar
    Science Advisor
    Homework Helper

    I don't think you need to do a lot of manipulation on a geometric series to find the sum. It should be pretty straightforward. Just factor out the k=1 term.
  4. Dec 15, 2008 #3
    I have factored out the k=1 term...yet, I still do not know exactly what to do. I wrote out the series for both the numerator and the denominator, yet I do not see what to do next.

    Here is my work:


    Another hint at the problem solving process will be greatly appreciated.

  5. Dec 15, 2008 #4


    User Avatar
    Homework Helper

    you could just write 2k+1=2k*2 and 5k-1=5k*5-1
  6. Dec 15, 2008 #5
    Thanks for all the hints....but now, I have another problem. I obtained an answer of 50/3...however, the solution booklet says the answer is 20/3...

    Here is my work:


    Is this a typo in the manual, or is my answer truly wrong? If so, please tell me where I messed up.
  7. Dec 16, 2008 #6


    User Avatar
    Homework Helper
    Gold Member

    The problem is that your sum is going from 1 to infinity, not zero to infinity. The formula for the geometric series that you used requires that the sum goes from zero to infinity:



Share this great discussion with others via Reddit, Google+, Twitter, or Facebook